Electric power-steering apparatuses that use an electric motor as an auxiliary power source are widely used for reducing the force required for operating a steering wheel when applying a steering angle to the steered wheels of an automobile (normally the front wheels except in special vehicles such as a forklift and the like). Electric power steering apparatuses having various constructions are known, and in all the kinds of constructions, auxiliary power from an electric motor is applied by way of a reduction gear to a steering shaft that is rotated by operating a steering wheel. Typically, a worm reducer is used as this reduction gear. In the case of an electric power-steering apparatus that uses a worm reducer, the auxiliary force from an electric motor is freely transmitted to the steering shaft by a worm that is rotated and driven by the electric motor engaging with a worm wheel that rotates together with the steering shaft.
FIG. 5 and FIG. 6 illustrate an example of a conventional electric power-steering apparatus. The front-end section of a steering shaft 2 is supported by the inside of a housing 3 so as to be able to rotate freely, and a worm wheel 4 is fastened to the front-end section of this steering shaft 2. A worm 7 that is fastened to an output shaft 6 of an electric motor 5 engages with this worm wheel 4. By the electric motor 5 rotating and driving the worm 7, auxiliary torque having a specified size and direction is applied to the worm wheel 4. The worm 7 comprises a worm shaft 8 and worm teeth 9 that are provided in the middle section in the axial direction of the outer circumferential surface of the worm shaft 8, and the base end section and the tip end section of the worm shaft 8 are supported inside the housing 3 by way of a pair of ball bearings 10a, 10b so as to be able to rotate freely. Moreover, a spline hole 11 that is open on the base end surface of the worm shaft 8 fit with the spline shaft section 12 that is provided on the tip end section of the output shaft 6 with a spline fit. On the other hand, the output shaft 6 is supported inside a motor case 13 by way of a pair of ball bearings 14a, 14b so as to be able to rotate freely.
During operation of this kind of electric power-steering apparatus, the electric current direction and amount supplied to the electric motor 5 is controlled according to the direction and size of the torque that is applied to the steering shaft 2 from the steering wheel 1. By applying appropriate auxiliary torque to the steering shaft 2 by way of the worm 7 and worm wheel 4, it is possible to transmit torque to a steering gear unit 16 by an intermediate shaft 15 that is greater than the torque that is inputted from the steering shaft 2. As a result, a pair of left and right tie rods 17 are pushed or pulled by a force that is larger than the operating force that is applied from the steering wheel 1, so it is possible to apply a desired steering angle to the left and right steered wheels even with a small operating force.
When doing this, the direction and size of the auxiliary torque frequently changes, so without taking various measures, beating noise or vibration is generated in the parts, and gives an unpleasant feeling to the passengers. Therefore, in the engaging section between the worn 7 and the worm wheel 4, by elastically pressing the ball bearing 10b on the tip end side of the worm 7 toward the worm wheel 4, backlash in this engaging section is eliminated and the generation of a gear rattling sound is prevented.
Moreover, placing an elastic member in between the tip end surface of the output shaft of the electric motor and the base end surface of the worm shaft, and suppressing backlash in the output shaft and worm by elastically pressing the output shaft and worm in directions away from each other is known (refer to JP2002-255047(A), JP2003-72563(A), JP2008-213667(A), JP2008-247190(A), JP2008-290693(A), and JP2009-61898(A)). Furthermore, JP2011-69495(A) discloses the use of a single-row deep groove four point contact ball bearing as the ball bearing for supporting the base end section of the worm shaft.
During operation of an electric power-steering apparatus, in order to suppress backlash that occurs due to minute displacement in the axial direction of the output shaft 6 of the electric motor 5, it is necessary to apply a preload to the pair of ball bearings 14a, 14b that support both end sections of the output shaft 6. In order to accomplish this, as illustrated in FIG. 7, a plate spring (disk spring, spring washer, wave washer or the like) 18 is provided between the base end surface (right end surface in FIG. 7) of the outer ring of the ball bearing 14a on the base end side of the output shaft 6 and the back end surface of the motor case 13. The elastic force of this plate spring 18, together with a face-to-face arrangement (DF) contact angle as indicated by the chain line in FIG. 7, applies a preload to the ball bearings 14a, 14b. 
In the case of this conventional construction, a force in the compression direction is repeatedly applied to the plate spring 18 during operation of the electric power-steering apparatus. In other words, as the worm wheel 4 and worm teeth 9 (see FIG. 6) engage, a reaction force from the engaging section is applied to the worm 7 that is provided with worm teeth 9. The direction in which the axial direction component of this reaction force acts is reversed each time the direction of the torque that is transmitted from the worm 7 to the worm wheel 4 changes. On the other hand, the ball bearing 14b on the tip end side of the output shaft 6, as can be clearly seen from the direction of the contact angles illustrated by the chain lines in FIG. 7, has very little function for supporting the component in the axial direction of the reaction force that acts in the direction from the worm 7 to the output shaft 6. Therefore, a force in the compression direction having nearly that magnitude is repeatedly applied to the plate spring 18 the number of times that the direction changes. As a result, from use over a long period of time, the elastic force of the plate spring 18 decreases or is lost, and thus the preload that is applied to the ball bearings 14a, 14b decreases or is lost. Particularly, the installation space for the plate spring 18 is limited, and for the elastic stroke (amount of change in the dimension in the axial direction in a state when an elastic force can be applied) of the plate spring 18, the percentage of the change in this dimension in the axial direction becomes large as the electric power-steering apparatus operates, so the elastic force of the plate spring 18 can easily decrease or be lost.
By providing an elastic member, for which a large elastic stroke compared to a plate spring can be easily maintained, between the tip end surface of the output shaft of the electric motor and the base end surface of the worm shaft as disclosed in JP08-290693(A), backlash in the axial direction of the output shaft is decreased a certain amount, however, is not sufficient. In other words, in the case of a conventional electric motor, both end sections of the output shaft are supported by a pair of ball bearings, and the directions of the contact angles that are applied to the balls of these ball bearings are opposite of each other. That is, a back-to-back arrangement (DB) contact angle or face-to-face arrangement (DF) contact angle is applied to these ball bearings. In either case, when the output shaft, which is supported so as to rotated freely by a pair of ball bearings of which the direction of the contact angles differ from each other, is pressed in the axial direction, the preload for one of the ball bearings increases and the preload for the other ball-bearing decreases. In the case where the preload of this other ball bearing is lost, there is a possibility that a strange noise, such as a beating noise, or vibration may occur in the portion of this other ball bearing. Therefore, by simply providing an elastic member between the tip end surface of the output shaft of the electric motor and the base end surface of the worm shaft, there is a problem in that it is not possible to sufficiently prevent backlash of the output shaft.